Answer:
26%
Step-by-step explanation:
To find the difference in the percent errors of the estimates, first find the percent error for each estimate.
To do this, we can use the Percent Error formula:
[tex]\boxed{\textsf{Percent Error} = \left| \dfrac{\textsf{Estimated Value} - \textsf{Actual Value}}{\textsf{Actual Value}} \right| \times 100\%}[/tex]
For the number of sheets of drywall, the estimated value is 18 and the actual value is 14. Therefore:
[tex]\textsf{Percent Error for drywall} = \left| \dfrac{18 - 14}{14} \right| \times 100\%\\\\\\\textsf{Percent Error for drywall} = \left| \dfrac{4}{14} \right| \times 100\%\\\\\\\textsf{Percent Error for drywall} = \dfrac{2}{7} \times 100\%\\\\\\\textsf{Percent Error for drywall} = 28.5714285714...\%\\\\\\\\[/tex]
For the square feet of tile, the estimated value is 65 and the actual value is 42. Therefore:
[tex]\textsf{Percent Error for tile} = \left| \dfrac{65 - 42}{42} \right| \times 100\% \\\\\\ \textsf{Percent Error for tile} = \dfrac{23}{42} \times 100\% \\\\\\ \textsf{Percent Error for tile} = 54.7619047619... \% \\\\\\[/tex]
The difference in percent errors is:
[tex]\textsf{Difference in percent errors} = \left|\textsf{Percent Error for drywall} - \textsf{Percent Error for tile}\right|[/tex]
Therefore:
[tex]\textsf{Difference in percent errors} = \left|28.5714285714...\% - 54.7619047619...\%\right|\\\\\\\textsf{Difference in percent errors}=26.190476190...\%\\\\\\\textsf{Difference in percent errors}=26\%[/tex]
So, to the nearest percent, the difference in the percent errors of the estimates is 26%.